Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | #626×AGL(1,𝔽11) |
| Hall | D11×#626 ⋊ C5 |
| Hall | C32×C11⋊C5 ⋊ C2×D4 |
| Hall | C32×C11 ⋊ C2×C5×D4 |
| Hall | C11⋊C5 ⋊ C2×#626 |
| Sylow | C11 ⋊ C2×C5×#626 |
| Sylow | C32 ⋊ D4×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×AGL(1,𝔽11) |
| commutator, Fitting, socle, cosocle | C2×C32×C11 | C23×C5 |
| hypocenter | C32×C11 | C2×C5×D4 |
| LCS | G ▷ C2×C32×C11 ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
496 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×#3811 |
| maximal normal subgroup of | AGL(1,𝔽11)×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.